Find the equation of a line through (1,3) and forming with the axes a triangle of area 6 square units. (Give three solutions).

Suppose the line has gradient . Then its equation is:

Simplify this, and then find the coordinates of the intercepts. They are:

and

Then, using base x height, write down an expression to represent the area of the triangle, and equate this to . (You need the sign, because you might have negative distances, and hence a negative area.

Re-write this as a pair of quadratic equations in (one equation for each of the two possible signs.)

Solve these to find the possible values of , and hence the equations of the lines.